10 citations · 16 across the 8 of their papers we have counts for
9 papers
Interactive Oracle Proofs of Proximity to Algebraic Geometry Codes
Sarah Bordage, Mathieu Lhotel, Jade Nardi +1
In this work, we initiate the study of proximity testing to Algebraic Geometry (AG) codes. An AG code over an algebraic curve is…
Standard Lattices of Compatibly Embedded Finite Fields
Luca De Feo, Hugues Randriam, Édouard Rousseau
Lattices of compatibly embedded finite fields are useful in computer algebra systems for managing many extensions of a finite field at once. They can also be used to…
Anticanonical codes from del Pezzo surfaces with Picard rank one
Régis Blache, Alain Couvreur, Emmanuel Hallouin +4
We construct algebraic geometric codes from del Pezzo surfaces and focus on the ones having Picard rank one and the codes associated to the anticanonical class. We give explicit co…
Gaps between prime numbers and tensor rank of multiplication in finite fields
Hugues Randriam
We present effective upper bounds on the symmetric bilinear complexity of multiplication in extensions of a base finite field Fp2 of prime square order, obtained by combining estim…
New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields
Julia Pieltant, Hugues Randriam
We obtain new uniform upper bounds for the (non necessarily symmetric) tensor rank of the multiplication in the extensions of the finite fields $\F_q$ for any prime or prime power…
Lower bounds on the minimum distance of long codes in the Lee metric
Hugues Randriam, Lin Sok, Patrick Solé
The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geome…